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For a large prime number p and a set A ⊂ F p we prove the following: (1) If A (A + A) does not cover all nonzero residues in F p , then | A | ⩽ p / 8 + o (p). (2) If A is both sum-free and satisfies A = A ⁎ , then | A | ⩽ p / 9 + o (p). (3) If | A | ≫ log ⁡ log ⁡ p log ⁡ p p , then | A + A ⁎ | ⩾ (1 + o (1)) min ⁡ (2 | A | p , p). Here the constants 1/8, 1/9, 2 are the best possible. Proofs make use of wrappers , subsets of a finite abelian group G , which 'wrap' popular values in convolutions of dense sets A , B ⊆ G. These objects carry certain structural features, making them capable of addressing additive-combinatorial and enumerative problems. [ABSTRACT FROM AUTHOR]

Copyright of Telecommunication Engineering is the property of Telecommunication Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

An intelligent protection scheme based on the single fuzzy inference system and discrete Fourier transform is proposed for the faulty phase detection and classification of faults on the mutually coupled double circuit transmission lines. This proposed protection technique uses the magnitude of the pre-processed current information of the sending end bus only. This is implemented in the MATLAB/Simulink environment on a 400 kV, 50 Hz, and 300 km double circuit power system model. The efficacy of the proposed scheme has been tested by performing a wide range of simulation studies concerning different types of faults (common short circuit faults, cross-country and evolving faults, and high impedance faults) and typical fault scenarios (current transformer saturation, noisy environment, and fault during power swing conditions) with variations in different fault parameters and operating conditions. The results presented confirm that the proposed method detects/classifies all the faults within one cycle time and is reliable with a detection/classification accuracy of 99.75%. It is immune to variations in fault parameters, and different operating conditions, and is not affected by the zero sequence mutual impedance. It does not require any training and communication link. Further, the performance is also appraised with other training-based protection schemes. [ABSTRACT FROM AUTHOR]

We propose a method for frequency domain feature analysis of point clouds based on the multilayer perceptron paradigm (MLP), named PFFA-MLP. By leveraging the Fourier transform and the latest MLP as a replacement for the transformer mechanism, PFFA-MLP maps point clouds to the frequency domain using a three-dimensional (3D) discrete Fourier transform. PFFA-MLP employs lightweight stacked DGCNN modules for initial feature extraction on multi-scale point cloud signals. It also includes a frequency domain feature analysis module, based on the MLP, which analyzes and aggregates the extracted multi-scale point cloud features. Point cloud understanding experiments are conducted on the ModelNet40, ScanObjectNN, and ShapeNet Part benchmarks. On ModelNet40, PFFA-MLP achieves an accuracy of 98% compared to PointMLP, while improving the detection speed by 7.2 times. On ScanObjectNN, the accuracy reaches 94% of PointMLP, while the detection speed is improved by 3.2 times. On ShapeNet Part, it achieves 97% of PointMLP. The experimental results demonstrate that PFFA-MLP achieves a favorable trade-off between training and inference speed. This method is applicable in scenarios that require efficient point cloud analysis while maintaining remarkable detection precision. [ABSTRACT FROM AUTHOR]

In this note, we study the convergence from the discrete to the continuous non-linear Fourier transform. Relations between spectral problems and questions in complex function theory provide a new approach to the study of scattering problems and the non-linear Fourier transform (see A. Poltoratski [Ann. of Math. (2) 199 (2024), pp. 741–793]). In particular, the non-linear Fourier transform can be viewed from the perspective of spectral problems for differential operators. Results of Makarov and Poltoratski [J. Lond. Math. Soc. 108 (2023), pp. 916–977] and Poltoratski and Zhang [J. Funct. Ana. 284 (2023), 29 pp.] can be seen as results for the non-linear Fourier transform. These results are similar to some convergence problems for the discrete non-linear Fourier transform considered by Tao [ An introduction to the nonlinear Fourier transform , 2002] and Tao and Thiele [ Nonlinear Fourier analysis , 2012]. [ABSTRACT FROM AUTHOR]

This paper presents an open-source time-dependent three-dimensional scalar photorefractive beam propagation model (PRProp3D) based on the well-known split-step method. The angular spectrum method is used for the diffractive steps, and the nonlinearities accumulated at the end of each diffractive step are applied using spatially varying phase screens. Comparisons with previously published experimental results are given for image amplification, photorefractive amplified scattering (fanning) and photorefractive screening solitons. Artifacts can be mitigated by use of step sizes less than 5~10 micrometers and by careful choice of the transverse computation grid size to ensure adequate sampling. Wraparound effects associated with the use of discrete Fourier transforms are mitigated by apodization and beam centering. [ABSTRACT FROM AUTHOR]

In this paper, we describe the associative and commutative algebra or the (2,2)-model of quaternions with application in color image enhancement. The method of alpha-rooting, which is based on the 2D quaternion discrete Fourier transform (QDFT) is considered. In the (2,2)-model, the aperiodic convolution of quaternion signals can be calculated by the product of their QDFTs. The concept of linear convolution is simple, that is, it is unique, and the reduction of this operation to the multiplication in the frequency domain makes this model very attractive for processing color images. Note that in the traditional quaternion algebra, which is not commutative, the convolution can be chosen in many different ways, and the number of possible QDFTs is infinite. And most importantly, the main property of the traditional Fourier transform that states that the aperiodic convolution is the product of the transform in the frequency domain is not valid. We describe the main property of the (2,2)-model of quaternions, the quaternion exponential functions and convolution. Three methods of alpha-rooting based on the 2D QDFT are presented, and illustrative examples on color image enhancement are given. The image enhancement measures to estimate the quality of the color images are described. Examples of the alpha-rooting enhancement on different color images are given and analyzed with the known histogram equalization and Retinex algorithms. Our experimental results show that the alpha-rooting method in the quaternion space is one of the most effective methods of color image enhancement. Quaternions allow all colors in each pixel to be processed as a whole, rather than individually as is done in traditional processing methods. [ABSTRACT FROM AUTHOR]

The clumping index (CI) is a key structural parameter that quantifies the nonrandomness of the spatial distribution of vegetation canopy leaves. Investigating seasonal variations in the CI is crucial, especially for estimating the leaf area index (LAI) and studying global carbon and water cycles. However, accurate estimations of the seasonal CI have substantial challenges, e.g., from the need for accurate hot spot measurements, i.e., the typical feature of the bidirectional reflectance distribution function (BRDF) shape in the current CI algorithm framework. Therefore, deriving a phenologically simplified stable CI product from a high-frequency CI product (e.g., 8 days) to reduce the uncertainty of CI seasonality and simplify CI applications remains important. In this study, we applied the discrete Fourier transform and an improved dynamic threshold method to estimate the start of season (SOS) and end of season (EOS) from the CI time series and indicated that the CI exhibits significant seasonal variation characteristics that are generally consistent with the MODIS land surface phenology (LSP) product (MCD12Q2), although seasonal differences between them probably exist. Second, we divided the vegetation cycle into two phenological stages based on the MODIS LSP product, ignoring the differences mentioned above, i.e., the leaf-on season (LOS, from greenup to dormancy) and the leaf-off season (LFS, after dormancy and before greenup of the next vegetation cycle), and developed the phenologically simplified two-stage CI product for the years 2001–2020 using the MODIS 8-day CI product suite. Finally, we assessed the accuracy of this CI product (RMSE = 0.06, bias = 0.01) via 95 datasets from 14 field-measured sites globally. This study revealed that the CI exhibited an approximately inverse trend in terms of phenological variation compared with the NDVI. Globally, based on the phenologically simplified two-stage CI product, the CILOS is smaller than the CILFS across all land cover types. Compared with the LFS stage, the quality for this CI product is better in the LOS stage, where the QA is basically identified as 0 and 1, accounting for more than ~90% of the total quality flag, which is significantly higher than that in the LFS stage (~60%). This study provides relatively reliable CI datasets that capture the general trend of seasonal CI variations and simplify potential applications in modeling ecological, meteorological, and other surface processes at both global and regional scales. Therefore, this study provides both new perspectives and datasets for future research in relation to CI and other biophysical parameters, e.g., the LAI. [ABSTRACT FROM AUTHOR]

Resistance spot welding (RSW) is a widespread technique for joining sheet metals. In industrial applications, working closely to expulsion conditions is common practice to maximize the welding size and, thus, the mechanical performance. On the other hand, expulsions lead to the worsening of mechanical characteristics, and the joint becomes visually unappealing. Manufacturing disturbance is another source of expulsion. Abnormal conditions like initial gap and edge proximity are one of the reasons for defects in mass production. This work proposes a procedure to quantify expulsion in RSW through an innovative index obtained from frequency domain analysis of the force signals acquired during the welding process. Furthermore, an indicator extracted from the displacement signals has been compared to the suggested expulsion index. An important finding of this study is that the presented index, in addition to identifying expulsion, indicates how close the process is to the expulsion limit, providing the possibility of recognizing possible shifts and trends that could arise from the actual process conditions. This leads to an effective tool for online process monitoring. Data from an experimental campaign performed to reproduce expulsion in case of inappropriate choice of process parameters, initial gap, and edge proximity validate the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

The article "Whistle Characteristics of the Rough-Toothed Dolphin (Steno bredanensis) in the Canary Islands" delves into the vocal behaviors of dolphins, specifically focusing on frequency-modulated whistles for communication and social coordination. The research underscores the significance of understanding dolphin acoustic communication and social structure through whistle characteristics, highlighting the adaptability of dolphins to environmental changes. By examining the bioacoustic behavior of rough-toothed dolphins in various regions, including the Canary Islands, Rio de Janeiro, and the Mediterranean Sea, researchers aim to provide valuable insights for conservation efforts. [Extracted from the article]

Spherical sheet steel molds filled with gray iron melts of varying chemical compositions and metallurgical conditions were air-cooled until solid, followed directly by austempering to preserve the austenite grain structure. The castings were studied using a combination of cooling curves and quantitative metallography, in order to clarify control of the austenite grain structure and its impact on the local microstructure. A novel method utilizing fast Fourier transform provided visual overview of macroscopic trends in the scale of the flake graphite structure. Castings inoculated with Sr-containing ferrosilicon featured finer eutectic cell structure but coarser equiaxed structure of austenite, emphasizing that melt treatments applied to control the graphite structure may have unintended effects on the austenite grain structure. In most non-inoculated castings, the microstructure was banded, with alternating layers of coarse and fine flake graphite with distance from the casting surface. The extent of the columnar zone of austenite grains showed no correlation with the graphite structure nor the volume fraction of dendrites. The volume-to-surface ratio of dendrites was more uniform in the columnar zone, but increased toward the center in the equiaxed zone. The casting with the highest carbon equivalent (4.34), featured zones containing finer dendrites and graphite. These zones appear to be gaps in the early solidification structure which filled later by secondary dendritic growth from surrounding austenite. This highlights that high carbon equivalent may lead to poor dendrite coherency which can make the microstructure less uniform and less predictable. [ABSTRACT FROM AUTHOR]

Purpose: Due to the continuous and rapid evolution of telecommunication equipment, the demand for more efficient and noise-robust detection of dual-tone multi-frequency (DTMF) signals is most significant. Design/methodology/approach: A novel machine learning-based approach to detect DTMF tones affected by noise, frequency and time variations by employing the k-nearest neighbour (KNN) algorithm is proposed. The features required for training the proposed KNN classifier are extracted using Goertzel's algorithm that estimates the absolute discrete Fourier transform (DFT) coefficient values for the fundamental DTMF frequencies with or without considering their second harmonic frequencies. The proposed KNN classifier model is configured in four different manners which differ in being trained with or without augmented data, as well as, with or without the inclusion of second harmonic frequency DFT coefficient values as features. Findings: It is found that the model which is trained using the augmented data set and additionally includes the absolute DFT values of the second harmonic frequency values for the eight fundamental DTMF frequencies as the features, achieved the best performance with a macro classification F1 score of 0.980835, a five-fold stratified cross-validation accuracy of 98.47% and test data set detection accuracy of 98.1053%. Originality/value: The generated DTMF signal has been classified and detected using the proposed KNN classifier which utilizes the DFT coefficient along with second harmonic frequencies for better classification. Additionally, the proposed KNN classifier has been compared with existing models to ascertain its superiority and proclaim its state-of-the-art performance. [ABSTRACT FROM AUTHOR]

As a typical multibody system, rolling bearing consists of several lubricated frictional pairs that transmit motions and forces among components. In this paper, a multibody lubrication dynamics (MLD) model of cylindrical roller bearings (CRBs) is developed by coupling the bearings dynamics submodel and several lubrication submodels of each frictional pairs in real-time. The lubrication submodels are discretized by using finite difference and solved by numerical iteration methods of Gauss-Seidel with line relaxation and discrete convolution-fast Fourier transform (DC-FFT) technique. Additionally, a parallel algorithm is also designed to enhance the calculation efficiency. Its results are validated by the experimental results in literature and further compared by the results from other dynamics models. It revealed that the film formation alters not only friction but also geometrical constraints and pressure distribution, which may introduce additional load inside bearing and increase rolling friction under high-speed conditions. As the dynamic oil film stiffness and damper are took into account by MLD, the cage has a lower whirl frequency and forces. The curve-fitting formulas of elastohydrodynamic lubrication (EHL) film thickness are overestimates of the thickness value and, thus, change the load distribution and friction between roller and raceway. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Mathematical Physics, Analysis, Geometry (18129471) is the property of B Verkin Institute for Low Temperature Physics & Engineering and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Mud pulse telemetry (MPT) systems are widely recognized for their effectiveness and are most commonly used to transmit downhole data to the surface in real time. These data facilitate the drilling process and make it more cost-efficient. In MPT, the mud channel presents a challenging communication environment, primarily due to various sources of noises, with pump noise being the most dominant. In this paper, a noise cancellation method based on discrete Fourier transform (DFT) is proposed for demodulation under a low signal-to-noise ratio, eliminating the pump noise generated by two pumps with a single sensor during drilling. The method employs DFT to estimate the noise spectrum, subtracts noises from the received signal, and performs an inverse transformation to reconstruct the original signal estimation. The effectiveness of the proposed method is evaluated through a simulation analysis and field experiments. The simulation results indicate that the major components of multiple pump noises could be successfully eliminated. The field experiment results demonstrate that the demodulation of the received data achieves advanced data rate communication and a low bit error rate (BER) in a 3000 m drilling system. [ABSTRACT FROM AUTHOR]

The high-precision signal writing machine, experiencing a 0.1% failure rate due to discrete fourier transform (DFT) of position error signal (PES) exceeding control limits, can be improved with an appropriate controller gain. This paper combines machine learning (ML) classification and controller optimization to determine the suitable gain for the hard disk drive (HDD) signal writing process. The result from machine classification has a high potential for position error improvement, distinguishing them from those with obvious degradation. The identified machine classes with high potential for signal write quality improvement undergo controller optimization using a genetic algorithm (GA). The objective function considers gain crossover frequency, phase margin, and PES DFT at low frequencies. Experimental results demonstrate that the new controller gain enhances signal write quality of class 0 and class 3 by 14.68% and 17.18%, respectively, leading to a reduced failure rate down to 0.05%. [ABSTRACT FROM AUTHOR]

Multipoint evaluation is the computational task of evaluating a polynomial given as a list of coefficients at a given set of inputs. Besides being a natural and fundamental question in computer algebra on its own, fast algorithms for this problem are also closely related to fast algorithms for other natural algebraic questions such as polynomial factorization and modular composition. And while nearly linear time algorithms have been known for the univariate instance of multipoint evaluation for close to five decades due to a work of Borodin and Moenck [7], fast algorithms for the multivariate version have been much harder to come by. In a significant improvement to the state-of-the-art for this problem, Umans [25] and Kedlaya & Umans [16] gave nearly linear time algorithms for this problem over field of small characteristic and over all finite fields, respectively, provided that the number of variables n is at most do(1) where the degree of the input polynomial in every variable is less than d. They also stated the question of designing fast algorithms for the large variable case (i.e., n x do(1)) as an open problem. In this work, we show that there is a deterministic algorithm for multivariate multipoint evaluation over a field Fq of characteristic p, which evaluates an n-variate polynomial of degree less than d in each variable on N inputs in time provided that p is at most do(1), and q is at most (exp(exp(exp(· · · (exp(d))))), where the height of this tower of exponentials is fixed. When the number of variables is large (e.g., n x do(1)), this is the first nearly linear time algorithm for this problem over any (large enough) field. Our algorithm is based on elementary algebraic ideas, and this algebraic structure naturally leads to the following two independently interesting applications: --We show that there is an algebraic data structure for univariate polynomial evaluation with nearly linear space complexity and sublinear time complexity over finite fields of small characteristic and quasipolynomially bounded size. This provides a counterexample to a conjecture of Miltersen [21] who conjectured that over small finite fields, any algebraic data structure for polynomial evaluation using polynomial space must have linear query complexity. We also show that over finite fields of small characteristic and quasipolynomially bounded size, Vandermonde matrices are not rigid enough to yield size-depth tradeoffs for linear circuits via the current quantitative bounds in Valiant's program [26]. More precisely, for every fixed prime p, we show that for every constant e > 0, and large enough n, the rank of any n × n Vandermonde matrix V over the field Fpa can be reduced to (n/exp(O(poly(e)log0.53 n))) by changing at most nT(e) entries in every row of V, provided a = poly(logn). Prior to this work, similar upper bounds on rigidity were known only for special Vandermonde matrices. For instance, the Discrete Fourier Transform matrices and Vandermonde matrices with generators in a geometric progression [9]. [ABSTRACT FROM AUTHOR]

In the ever-evolving landscape of wireless communication, there is a persistent quest for modulation schemes that optimize spectral efficiency, reduce interference, and enhance overall system performance. This paper introduces a novel modulation technique that synergistically improves on the strengths of filter bank multi-carrier (FBMC). A distinctive feature of our approach is the deployment of the Hermite prototype filter in the FBMC system, diverging from traditional FBMC architectures. An advanced precoding strategy leveraging a pruned discrete fourier transform (pDFT) paired with scaling is also introduced. This combination promises reduced inter-symbol interference and heightened spectral efficiency. As the management of the peak-to-average power ratio (PAPR) is a significant challenge in FBMC systems to addressing this iterative particle swarm optimization (IPSO) algorithm is proposed. Evaluations are carried out to demonstrate the efficiency of the proposes scheme in reducing PAPR substantially for FBMC/OQAM framework. Experiments are conducted and comparisons are performed among several prominent multicarrier modulation schemes. The results from the experiments indicate that the application of IPSO algorithm with Hermite functions and applied to an FBMC/OQAM system using pruned DFT has been successful in reducing the PAPR also a 6-13% decrease in error rate has been shown across varying QAM orders regardless of SNR level. [ABSTRACT FROM AUTHOR]

This paper presented an extended double-subsegment discrete Fourier transform (DS-DFT) algorithm as a tool for the fine spectral estimation of high-noise environments, which was previously effective in low-noise scenarios, and as such, its application to the analysis of noisy signals observed by a satellite-based interferometer was investigated. The observation of satellite-borne Doppler asymmetric spatial heterodyne spectroscopy (DASH) was first simulated to obtain the signals of low- and high-noise levels; then, a practical criterion to classify noise levels in the interferograms based on the DS-DFT results was introduced and validated by calculating the SNR. For high-noise signals, DS-DFT remains robust by employing phase differences and amplitude ratios for fine frequency estimation. [ABSTRACT FROM AUTHOR]

ABSTRACT Harmonic gears are widely used in precise space technology, robotic, medical equipment and other fields, while the magnitude of surface topography changes due to wear is usually comparable to or larger than the original surface roughness and elastic deformation, leading to severe transmission failures. This paper reports a numerical approach to simulate the lubrication status considering wear evolution based on mixed elastohydrodynamic lubrication (EHL) and Archard models, in which the Reynolds equation is solved with finite difference method and surface deformation is calculated by the discrete convolution‐fast Fourier transform (DC‐FFT) algorithm. The interfacial pressure and film thickness distributions are validated by comparison with available results from literature. The harmonic gear lubrication and wear performances are calculated, including effects of machined surface, velocity, load, wear time and material properties, and the results suggest that avoiding long‐term and high‐torque working with a large wear coefficient can effectively prevent surface wear failure, which is beneficial for increasing the harmonic gears' lifespan. [ABSTRACT FROM AUTHOR]

Designing mechanical metamaterials to control wave propagation often requires extensive finite element analysis and discrete Fourier transform simulations before fabricating 3D printed structures and conducting experiments. Here, an alternative approach is presented to developing a metamaterial informatics framework by integrating dataset collection with artificial intelligence (AI), which can significantly accelerate the advancement of phononic wave chip technologies based on the triply periodic minimal surface (TPMS). Visualized data analysis is performed to evaluate the sensitivity of phononic band frequency numbers (BNF). Subsequently, various machine learning algorithms are compared for the prediction of sonic BNFs to create a unique identificable encoded mechanical identification tag (EMIT) interacting with sound waves. Then, for the mechanical decoding part with the help of acoustic analogy, a novel concept technology is developed that integrates 3D‐printed EMITs with a deep‐learning audio classifier for the ownership identification of instruments. Underwater application is discussed further for civil accident investigations, such as echolocating missing aircraft, divers, sunken ships, and containers with valuable cargo. These TPMS‐based EMITs represent the first‐generation passive sonic frequency identification (SFID) transponder‐tags, marking the advent of SFID transponder systems. [ABSTRACT FROM AUTHOR]

The fast Fourier transform (FFT) is a widely used algorithm for computing the discrete Fourier transform (DFT) in real-time signal processing. Achieving high performance with minimal resource usage is crucial for any real-time application. This paper introduces an architecture based on coordinate rotation digital computer (CORDIC) for implementing a radix- 2 2 FFT. Traditional FFT implementations require complex twiddle factor multiplications, which is not cost-effective in terms of hardware utilization. To address this issue, we have proposed a radix-8 CORDIC-based approach integrated with FFT computation. The proposed radix-8 CORDIC requires fewer stages than the conventional radix-2 CORDIC, enhancing computational efficiency and reducing hardware utilization. The feedforward radix- 2 2 FFT architecture is presented where the butterflies of the FFT are computed with the help of radix-8 CORDIC. A total of three FFT architectures are developed supporting 16-, 1024- and 2048-point FFTs. The proposed FFT architectures are developed using Verilog-HDL code and implemented on a Virtex-7 field-programmable gate array (FPGA). The FPGA-based radix- 2 2 FFT achieves a clock frequency of 323.4 MHz and utilizes minimal FPGA resources. Processing of 2048 data samples takes only 4.06 μ S by the proposed FPGA-based design. Additionally, two ASICs have been designed: the 1024-point FFT ASIC occupies an area of 1.079 mm2, and the 2048-point FFT ASIC occupies an area of 1.544 mm2. The proposed FFT ASICs have better-normalized area per FFT and energy per FFT than the state-of-the-art designs. [ABSTRACT FROM AUTHOR]

Due to the high power density and wide speed range, a permanent magnet synchronous motor (PMSM) is commonly used in industry. Efficient production requires optimized motion control of the mechanism driven by the PMSM. Unfortunately, designing the controller is usually based on a model of the mechanism without including parameters originating from the motor. Cogging stiffness originates from the magnetic forces between rotor magnets and stator teeth and is one of these forgotten parameters. The performance is sub-optimal when this stiffness is not considered during control design. The stiffness also changes over time due to changing load conditions such as temperature. Aiming for optimized motion control of high-speed mechanisms, this article proposes to expand the classic motion controller with an on-line stiffness tracker. The tracker is based on the sliding discrete Fourier transform (SDFT). The tracking technique is conceptually analyzed and experimentally validated on a PMSM-driven rod. The classic Welch technique having an update time of at least 100 s is used as a benchmark. With similar accuracy and a much faster update time of 1.25 ms, the stiffness is tracked on-line using SDFT. The developed stiffness tracker is implemented on the provided commercial motion controller, proving its computational efficiency. [ABSTRACT FROM AUTHOR]

In this paper, we propose a hybrid relay-reflecting intelligent surface (HR-RIS)-assisted cell-free (CF) massive multiple-input multiple-output (mMIMO) network to achieve consistent spectral efficiency (SE). The HR-RIS technique manipulates the propagation environment by reflecting and enhancing radio signals in desired locations, providing a symbiotic integration with CF mMIMO for future wireless communication systems. We first model uplink and downlink channels, obtaining minimum-mean-square-error estimations for efficient transmission paths. We then analyze the SE performance of the proposed system. To enhance sum spectral efficiency in downlink multi-antenna, multi-user, and millimeter-wave massive MIMO networks, we introduce a low-complexity hybrid precoding approach. The optimal analog equalizer is determined by converting the analog precoding matrix dimensions into square matrices and selecting a few discrete Fourier transforms to maximize the amplitude of corresponding wideband channel matrices. We employ the equal gain transmission technique to combine channel gains efficiently and ensure spectral efficiency. To mitigate inter-user interference, we propose an enhanced block diagonalization method for designing the digital precoder and combiner. Our study demonstrates that the proposed HR-RIS-assisted CF mMIMO system offers significant improvements in SE performance, paving the way for advanced wireless communication systems. [ABSTRACT FROM AUTHOR]

Conventional B0 gradient systems have several weaknesses including high cost and bulk. As a step towards addressing these while providing new degrees of freedom for spatial encoding and system design in Magnetic Resonance Imaging (MRI), a radio frequency (RF) gradient encoding system and pulse sequence for phase encoding using the Bloch–Siegert (BS) shift were developed. Optimized BS spatial encoding coils with bucking windings (counter‐wound loops) were designed and constructed, along with compatible homogeneous imaging coils for excitation and signal reception. Two coil systems were developed: one for phantom imaging and a second for human wrist imaging. BS phase‐encoded imaging and BS RF pulse simulations were performed. Pulse sequences were designed for linear stepping in k‐space and implemented on a 47.5‐mT scanner to image resolution phantoms in both coil setups. Reconstructions were performed using both the full B1+‐based encoding fields for each BS pulse amplitude and using inverse discrete Fourier transforms. A B0 gradient was used for frequency encoding during signal readout, and the third axis was projected. Specific absorption ratio (SAR) calculations were performed for the wrist coil to determine the safety of BS‐based RF encoding for B0 fields in the low field MRI regime. The optimized RF spatial encoding coils resulted in higher linearity (R2=0.9981 and 0.9921 in the phantom and wrist coils, respectively) than coils used in previous work. The phantom and wrist imaging coils were validated in simulations and experimentally to produce a peak B1+=1.35 G and 0.8 G with 12‐W input power, respectively, in the field‐of‐view (length = 11 cm) used for imaging. Nominal imaging resolutions of 5.22 and 7.21 mm were, respectively, achieved by the two‐coil systems in the RF phase‐encoded dimension. Coil systems, pulse sequences, and image reconstructions were developed for linear RF phase encoding using the BS shift and validated using a 47.5‐mT open low field scanner, establishing a key component required for B0 gradient‐free imaging at low B0 field strengths. [ABSTRACT FROM AUTHOR]

This study utilized passive acoustic emissions from a fluidized bed containing spherical inert ABS particles, captured by an external piezoelectric microphone, to monitor fluidization agitation intensity. Acoustic signals were recorded during fluidization profiles achieved under air velocities ranging from 0.5 to 3.0 m/s and during the drying of water or maltodextrin aqueous solution (1:5 w/w) introduced as droplets. Analyzing audio features like waveforms, the Discrete Fourier Transform (DFT), and Mel Frequency Cepstral Coefficients (MFCCs) revealed changes corresponding to the agitation intensity of the particles. The MFCC coefficients were input into a three-layer artificial neural network (ANN) to predict fluidization dynamics based on air velocity, liquid flow rate, and drying time. The ANN efficiently learned from the data, achieving high predictive accuracy (R2 > 0.8) after 15 epochs of training, showcasing the robustness of MFCC coefficients for modeling. This approach highlights that the application of passive acoustic signals and neural networks allows for real-time monitoring of fluidization behavior during drying processes. [ABSTRACT FROM AUTHOR]

The quaternion discrete Fourier transform (QDFT) is a powerful tool in modern digital signal processing, even though until recently this transformation seemed exotic. In recent years, quite a lot of publications have appeared devoted to effective ways to calculate this transformation. In particular, in one of our previous publications, we presented an economical algorithm for calculating one-dimensional QDFT and showed that this algorithm has the lowest computational complexity among all known algorithms of this type. This generalized algorithm is suitable for computing the QDFT of any sequence in which the number of elements is a power of two. However, as it turned out, there are additional possibilities that make it possible to further reduce the computational complexity of the developed algorithm for each specific N. In this article, we provide some examples of the synthesis of such algorithms for short-length input sequences (samples of signals). In particular, algorithms for N ∊ {2, 3, 4, 5, 6, 7, 8} are presented. A parallel implementation of the proposed algorithm allows for saving more than half of the number of required multipliers in each case compared with the parallel implementation of the naive methods of calculation. [ABSTRACT FROM AUTHOR]

The adaptive backstepping method has strong performance in handling control problems with disturbances in previous research. However, it exhibits limitations when applied to time-varying disturbances. This paper proposes an improved adaptive backstepping method based on Discrete Fourier Transform (DFT). By estimating the frequency spectrum of the disturbance and indirectly obtaining its time-domain estimate, the proposed method effectively overcomes the shortcomings of traditional adaptive backstepping. To address the issue of frequency leakage caused by discontinuities in window data, the idea of DFT is improved by using STFT with the addition of the window function and window-shifting operation. Additionally, a projection operator and adaptive reduction of the control objective are employed to mitigate the effects of actuator saturation. Finally, in simulations involving an aircraft subjected to gusts and turbulence, the proposed method is compared with traditional adaptive backstepping and radial basis function (RBF) neural network control methods. Simulation results demonstrate that the proposed method outperforms the others in these experimental scenarios. [ABSTRACT FROM AUTHOR]

The majority of Digital Audio Tampering Detection (DATD) methods, which are based on Electrical Network Frequency (ENF), predominantly concentrate on the static spatial information of ENF. Unfortunately, this focus neglects the temporal variation present in the ENF time series. This limitation significantly hampers the ENF feature representation capability, consequently diminishing the overall accuracy of tampering detection. To address this gap, our paper introduces an innovative digital audio tampering detection method founded on ENF spatio-temporal feature representation learning. To enhance the feature representation capability and subsequently improve tampering detection accuracy, we propose the construction of a parallel spatio-temporal network model. This model incorporates both Convolutional Neural Network (CNN) and Bidirectional Long Short-Term Memory (BiLSTM) network architectures. Through this hybrid model, we aim to deeply extract both ENF spatial and temporal feature information. In the process of extracting spatial and temporal features of ENF, we utilize high-precision Discrete Fourier Transform (DFT) analysis on digital audio. This analysis allows us to extract ENF phase sequences, which are then adaptively divided into frames through frame shifting. The result is feature matrices of uniform size, effectively representing the spatial features of ENF. Concurrently, phase sequences are segmented into frames based on ENF time changes to capture the temporal features of ENF. Subsequently, deep spatial and temporal features are extracted using CNN and BiLSTM, respectively. To further enhance the representation capability of the spatio-temporal features, we introduce an attention mechanism. This mechanism dynamically assigns weights to the deep spatial and temporal features, providing a nuanced and refined representation. Finally, a deep neural network is employed to discern whether the audio has undergone tampering. Our experimental results validate the effectiveness of our approach, showcasing superior performance compared to six state-of-the-art methods across three public databases for digital audio tampering detection. This comprehensive methodology, focusing on both spatial and temporal aspects of ENF, establishes a robust foundation for advancing the field of DATD and contributes significantly to improving detection accuracy. [ABSTRACT FROM AUTHOR]

Phasor estimation plays a critical role in island detection, fault detection, voltage stability monitoring, and state estimation within power systems. This paper proposes a phasor estimation method using micro-Phasor Measurement Units (µPMUs) in a Smart Distribution Network. A µPMU model is developed utilizing a recursive Discrete Fourier Transform (DFT) algorithm combined with high-precision filters to enhance accuracy. The optimal placement of µPMUs in the distribution network is determined using a Mixed-Integer Linear Programming (MILP) approach for the IEEE 33 bus test system. The model is tested on the IEEE 33 bus system with Electric Vehicle Charging Stations (EVCS) and Distributed Generators (DGs) under both nominal and off-nominal frequencies. The results comply with the IEEE C37.118.1 standard, achieving phasor magnitude errors as low as + 0.01% and frequency accuracy of 1 mHz with minimal ripple. This study demonstrates the robustness and precision of the µPMU model, highlighting its potential for enhancing real-time monitoring and control in smart grid applications. [ABSTRACT FROM AUTHOR]

Human pluripotent stem cells (hPSCs) attract tremendous attention due to their unique properties. Manual extraction of trajectories of cell colonies in experimental image time series is labor intensive and subjective, thus the aim of the work was to develop a computer semi-automated protocol for colony tracking. The developed procedure consists of three major stages, namely, image registration, object detection and tracking. Registration using discrete Fourier transform and tracking based on the solution of a linear assignment problem was implemented as console programs in the Python 3 programming language using a variety of packages. Object detection was implemented as a multistep procedure in the ProStack in-house software package. The procedure consists of more than 40 elementary operations that include setting of several biologically relevant parameters, image segmentation and performing of quantitative measurements. The developed procedure was applied to the dataset containing bright-field images from time-lapse recording of the human embryonic cell line H9. The detection step took about 6 h for one image time series with a resolution of 2560 by 2160; about 1 min was required for image registration and trajectories extraction. The developed procedure was effective in detecting and analyzing the time series of images with "good" and "bad" phenotypes. The differences between phenotypes in the distance in pixels between the starting and finishing positions of trajectories, in the path length along the trajectory, and the mean instant speed and mean instant angle of the trajectories were identified as statistically significant by Mann–Whitney and Student's tests. The measured area and perimeter of the detected colonies differed, on average, for different phenotypes throughout the entire time period under consideration. This result confirms previous findings obtained by analyzing static images. [ABSTRACT FROM AUTHOR]

Quasi-zero-stiffness (QZS) isolator has great application potential in the field of low-frequency vibration isolation due to its high-static and low-dynamic (HSLD) nonlinear stiffness characteristic, but it is precisely this characteristic that makes it very sensitive to load changes. Once the load changes, causing it to deviate from the equilibrium position, it no longer qualifies zero-stiffness characteristic, and the vibration isolation capacity will be significantly decrease. To make the QZS isolator possess variable load capacity and be more suitable for engineering practice, an active QZS vibration isolator based on electromagnetic actuator is designed in this paper, which eliminates the influence of load changes through the active force of the electromagnetic actuator. First, the dynamic equation of the isolator is established by Newton–Euler method, and the dynamic characteristic of the isolator under standard load and load variations are analyzed through improved incremental harmonic balance (IHB) method based on discrete Fourier transform (DFT). Next, the improved particle swarm optimization (PSO) algorithm are employed to optimize the Proportion Integration Differentiation (PID) controller parameters. Then, the vibration isolation performance of QZS isolator in controlled and uncontrolled and linear systems in the same control state are compared in frequency domain and time domain, respectively. Finally, the performance of active QZS isolator under load variation is discussed. The results indicate that the isolation performance of the QZS isolator under active control is significantly better than in uncontrolled conditions and the controlled linear system. When the load changes, real-time compensation through the actuator output control force can also enable the QZS isolator to achieve a better vibration isolation performance. [ABSTRACT FROM AUTHOR]

ABSTRACT Functionally graded coating (FGC) has played a pivotal role in numerous engineering applications owing to its exceptional properties. This work proposes a novel elastohydrodynamic lubrication (EHL) model with FGC, in which the elastic deformation and stress are computed using influence coefficients (ICs) and discrete convolution‐fast Fourier transform (DC‐FFT) algorithm. Comparisons are made with homogeneous EHL solutions and finite element analysis (FEA) to validate its accuracy. The study systematically explores how coating elastic modulus, coating thickness and substrate elastic modulus influence contact and lubrication behaviours. The developed model is expected to establish a theoretical framework for FGC material design, enhancing the performance of friction pairs. [ABSTRACT FROM AUTHOR]

In this paper, the discrete octonion linear canonical transform (DOCLCT) is presented. According to the definition of DOCLCT, its shift transform and modulation transform are explored. In addition, based on a new convolution operator, we obtain the convolution theorem of DOCLCT. The DOCLCT can be derived by the three-dimensional (3D) linear canonical transform. So, the fast algorithm of 3D DOCLCT is discussed. Finally, Heisenberg's uncertainty principle associated with DOCLCT is established. [ABSTRACT FROM AUTHOR]

The concept of Compressive Sensing (CS), which emerged in the 2000s, is about the existence of sparse states of signals in a transformation area other than the time axis or the axis they exist. Primary data organized in accordance with the purpose or secondary data collected in accordance with the purpose can be expressed sparsely in a size appropriate to the data structure. The CS method, which is applied to randomly collected data from the sparse form created as a result of the transformation, provides an advantage in cases where sample collection from the signal is difficult, incomplete and costly. When the total amount that can be taken is defined as 100%, the reconstruction algorithm is applied to the amount taken below this amount and called the measurement, and a signal close to the original of the signal is obtained. This study is about CS method to Frequency Modulated Continuous Wave Radars (FMCWR) based on Discrete Fractional Fourier Transform (DFrFT). The degree of FrFT is estimated with the first few scans of the FMCWR and the signal is randomly received in the amount of 25% in the next scans. In the reconstruction phase, the l1 norm of convex optimization is applied and its success is tested. When the most appropriate degree is determined as a result of degree estimation and the method is applied to 25% of the randomly collected signal; It can be seen that even whe n 75% of the signal is not received, very high performance is achieved in reconstructing the signal. This performance was compared with other fraction degrees and the results were expressed in a table. [ABSTRACT FROM AUTHOR]

This paper introduces a class of stochastic processes making jumps around the circle. These circular processes are the wrapped versions of the Poisson, the negative binomial, the binomial processes and of extensions thereof obtained by compounding with a secondary frequency distribution. Their prevailing application is for modeling planar motions. These processes can be weakly stationary, can have uniform stationary distribution, can have independent or stationary circular increments. Their autocovariance functions, one-dimensional trigonometric moments and wrapped distributions are obtained. For the wrapped Poisson process, it is shown that the formula for the one-dimensional distribution can be obtained either by discrete Fourier transform or by wrapping the Poisson distribution around the circle and by simplifying it with the generalized hyperbolic function. Some numerical illustrations and comparisons are provided. [ABSTRACT FROM AUTHOR]

This study proposes a novel forgery detection method based on the analysis of frequency components of images using the Discrete Fourier Transform (DFT). In recent years, face manipulation technologies, particularly Generative Adversarial Networks (GANs), have advanced to such an extent that their misuse, such as creating deepfakes indistinguishable to human observers, has become a significant societal concern. We reviewed two GAN architectures, StyleGAN and StyleGAN2, generating synthetic faces that were compared with real faces from the FFHQ and CelebA-HQ datasets. The key results demonstrate classification accuracies above 99%, with F1 scores of 99.94% for Support Vector Machines and 97.21% for Random Forest classifiers. These findings underline the fact that performing frequency analysis presents a superior approach to deepfake detection compared to traditional spatial detection methods. It provides insight into subtle manipulation cues in digital images and offers a scalable way to enhance security protocols amid rising digital impersonation threats. [ABSTRACT FROM AUTHOR]

Spontaneous breathing trials (SBTs) represent a pivotal phase in the weaning process of mechanically ventilated patients. The objective of these trials is to assess patients' readiness to resume independent breathing, thereby facilitating timely weaning and reducing the duration of mechanical ventilation (MV). Nevertheless, accurately predicting the success or failure of SBT remains a significant challenge in clinical practice. This study proposes a healthcare system that employs machine learning techniques to predict the outcome of SBT. The model is trained on respiratory flow and electrocardiogram (ECG) signals, employing the non-uniform discrete Fourier transform (NUDFT) for frequency domain analysis. The SBT prediction model has the potential to significantly enhance clinical decision-making by enabling the early identification of patients at risk for SBT failure, achieving an accuracy of 84.4 ± 3.2%. [ABSTRACT FROM AUTHOR]

This study estimates the direction of radio signals radiated by high-speed mobile platforms and analyzes detection performance using a frequency-invariant multisystem for broadband direction finding (DF). The discrete Fourier transform (DFT)-based frequency-invariant beamforming (FIB) algorithm was used to generate a constant beam pattern regardless of the frequency utilized. DFT-based FIB enables the rapid derivation of FIB weights. When applying FIB to a monopulse, a wide unambiguous range can be achieved. This can be used for monopulse DF that utilizes auxiliary systems. When the unambiguous region of the monopulse is narrower than the error of the auxiliary system, the DF errors increase. However, by employing FIB, a broader unambiguous region can be achieved, enhancing DF accuracy. The monopulse receiver example in this study was composed of 16 elements and detected arbitrary signals in the range of 6∼20 GHz. Assuming a single-system setup with an incoming signal within ±30°, the system showed a DF error of 1.04° at an SNR of 20°dB. With a multi-system setup and a ±45° incoming signal range, the error was reduced to 3.82° at an SNR of 5 dB. [ABSTRACT FROM AUTHOR]

As the core operation of lattice cipher, large-scale polynomial multiplication is the biggest computational bottleneck in its realization process. How to quickly calculate polynomial multiplication under resource constraints has become an urgent problem to be solved in the hardware implementation of lattice ciphers. Therefore, an analog in-memory circuit for fast polynomial multiplication calculation is proposed. First, an in-memory computing circuit for Discrete Fourier Transform and Inverse Discrete Fourier Transform based on memristor array is designed. On this basis, a fully analog circuit that can realize polynomial multiplication in one step is designed. Compared with traditional hardware implementation, the in-memory calculation method used in this article decreases the calculation time of polynomial multiplication to the microsecond level, which greatly improves the speed of lattice cipher encryption and decryption. For the specific examples in this article, PSPICE simulation shows that the average accuracy of the calculation result is above 99.90%. [ABSTRACT FROM AUTHOR]

In light of the escalating demand for computing powers, wave‐based analog computers have emerged as a compelling study area due to their remarkable capacity for ultra‐fast operation. Here, a programmable wave‐based computer, based on programmable meta‐structures is proposed, which is also called as meta‐computer. The meta‐computer can perform various types of analog computations in real‐time in the electromagnetic (EM) wave space, including matrix‐vector multiplication, discrete Fourier transform, filtering, and solving complex matrix equations. Owing to the powerful capability of the programmable meta‐structures in manipulating the EM fields and waves in real‐time, the proposed meta‐computer exhibits the advantages of flexible re‐programmability, low complexity, and direct computation in the EM space. Two prototypes of the meta‐computer in the microwave frequency are designed and fabricated, and the computing capability is validated through both numerical simulations and experiments. This work contributes a prominent approach for fully programmable wave‐based computers with noteworthy implications for expanding the applications of analog computing. [ABSTRACT FROM AUTHOR]

By applying vision sensing to realize online intelligent control on the pipeline welding process, the welding efficiency and qualification rate of pipeline girth butt joint during on-site construction of long-distance oil and gas pipelines can be effectively improved. During the pipeline external welding process, based on the designed combined line structured lights vision sensor (C-LSLVS), a partitioned time–frequency-space (PTFS) image processing algorithm is proposed to extract the laser centerline for the deformed laser lines image of double-V composite groove. The algorithm first utilizes information in the time domain to remove random interference from the image, and then, based on Radon transform (RT) and discrete Fourier transform (DFT), other stationary interferences can be eliminated and laser line characteristics can be enhanced by back-projection reconstruction in the frequency domain and space domain, so the stable and accurate extraction of laser centerline can be achieved under different situations. Subsequently, the theoretical analysis and error calculation of the pipeline groove sizes and related parameters solution model based on the local plane fitting method are carried out, and high-precision calculations of the parameters are completed. Finally, an intelligent pipeline welding system based on the C-LSLVS is constructed. In the intelligent welding experiment, the maximum detection error of the pipeline welding groove sizes did not exceed 0.20 mm, and the weld seam tracking deviation did not exceed 0.25 mm. The welding results show that the system has important application value for the development of pipeline intelligent welding. [ABSTRACT FROM AUTHOR]

The Discrete Cosine Transform (DCT) can be used instead of the conventional Discrete Fourier Transform (DFT) for the Orthogonal Frequency Division Multiplexing (OFDM) construction, which offers many advantages. In this paper, the Multiple-Input-Multiple-Output (MIMO) DCT-OFDM is enhanced using a proposed Cosine Domain Equaliser (CDE) instead of a Frequency Domain Equaliser (FDE). The results are evaluated through the Rayleigh fading channel with Co-Carrier Frequency Offset (Co-CFO) of different MIMO configurations. The average bit error probability and the simulated time of the proposed scheme and the conventional one are compared, which indicates the importance of the proposed scheme. Also, a closed formula for the number of arithmetic operations of the proposed equaliser is developed. The proposed equaliser gives a simulation time reduction of about 81.21%, 83.74% compared to that of the conventional Linear Zero Forcing (LZF)-FDE and Linear Minimum Mean Square Error (LMMSE)-FDE, respectively, for the case of a 4 × 4 configuration. [ABSTRACT FROM AUTHOR]

Mid-frequency transmissions (1.5 to 7.5 kHz) from a towed source to a drifting array one convergence zone away demonstrate smoothly varying phase. Calculations of the strength and diffraction parameters Φ and Λ for a representative background environment predict partially saturated propagation. For a single convergence zone path, the evolving phase rate due to the changing internal wave field corresponds to a narrowband coherent integration time, defined by the length of a discrete Fourier transform that likely captures the signal, from ∼370 s at 10 kHz to ∼1370 s at 1 kHz in the absence of source motion. Simulated propagation with a split-step parabolic equation solver through a sound speed field with thermocline fine structure and a Garrett-Munk internal wave displacement field provides a full wave picture that is consistent with the statistical predictions. Experimental data from the Philippine Sea demonstrates signal phase that is highly correlated with source tow body vertical excursions, measured by a pressure sensor, that couple into horizontal motion. The received signal can be integrated for up to 128 s at 5.5 kHz, with the upper limit thought to be due to non-uniform source motion rather than ocean dynamics. [ABSTRACT FROM AUTHOR]

We verify the recently developed method by Kisil (Kisil 2024 SIAM J. Appl. Math. 84, 464-476 (doi: 10.1137/23M1562445)) through its application in the study of the anti-plane dynamic response of an elastic square-cell lattice quadrant having a free lateral boundary that is subjected to a sinusoidal point load. The vertical boundary of the quadrant is assumed to be either fixed or free. The approach adopted utilizes the discrete Fourier transform in both principal lattice directions to reduce the governing equations to a functional equation linking both the bulk and boundary response of the system. For both problems, this functional equation is shown to reduce to scalar Wiener-Hopf equation whose solution can be exploited to determine the full response of the lattice system. The analytical solutions based on the Wiener-Hopf method are also implemented in numerical investigations that demonstrate the lattice response to various positions and frequencies of the load. In particular, this study includes dynamic regimes induced by the load that possess strong anisotropy and shows how the associated waveforms interact with the boundaries of the quadrant. [ABSTRACT FROM AUTHOR]

An extension of the tight‐binding approximation model using the discrete fractional Fourier transform is proposed. The quantum state between localized and delocalized states is formulated, where the intermediate state is continuously parameterized. The mixed features of the localized molecular‐like state and delocalized wave‐like state are confirmed when the wavefunction and band diagram of the intermediate state are represented. The proposed model is expected to be used to represent the quantum state with localized/delocalized features in, for example, organic semiconductors. [ABSTRACT FROM AUTHOR]

Bearings play a key role in rolling mills, and the uniformity of their lubricant film directly affects the degree of wear of bearings and the safety of equipment. Due to long-term stress, the lubricant film inside the bearing is not uniformly distributed, resulting in uneven wear between the journal and the shaft tile, which increases the potential safety hazards in production. Traditional disassembly inspection methods are complex and time-consuming. Ultrasonic nondestructive testing technology, which has the advantages of nondestructive and adaptable, has become an effective means of assessing the thickness of the oil film in bearings. In this study, an experimental platform for calibrating the lubricant film thickness in bearings was constructed for the first time, and the acoustic characteristics of different thicknesses of the oil film were measured using ultrasonic detection equipment to verify the accuracy of the simulation process. The experimental results show that after discrete Fourier transform processing, the main features of the frequency channels of the reflected acoustic signals of different thicknesses of the oil film are consistent with the finite element simulation results, and the errors of the oil film thicknesses calculated from the reflection coefficients are within 10% of the set thicknesses, and the measurement ranges cover from 5 μm to 250 μm. Therefore, the above method can realize the accurate measurement of the thicknesses of the oil film in bearings. [ABSTRACT FROM AUTHOR]

In this work, we initially construct an implicit Euler difference scheme for a two-dimensional heat problem, incorporating both local and nonlocal boundary conditions. Subsequently, we harness the power of the discrete Fourier transform and develop an innovative transformation technique to rigorously demonstrate that our scheme attains the asymptotic optimal error estimate in the maximum norm. Furthermore, we derive a series of approximation formulas for the partial derivatives of the solution along the two spatial dimensions, meticulously proving that each of these formulations possesses superconvergence properties. Lastly, to validate our theoretical findings, we present two comprehensive numerical experiments, showcasing the efficiency and accuracy of our approach. [ABSTRACT FROM AUTHOR]

The liver viability monitoring during its procurement is critical to guarantee the safe liver transportation. Traditionally, the viability is assessed by taking invasive biopsy on the liver surface. Recently, the noninvasive thermal images of liver surface have been used as an alternative assessment way. Researchers have proposed monitoring and classification approaches based on the thermal images. Existing works have demonstrated the importance of the temporal variation or the spatial variation of the thermal images to the viability monitoring. However, there is no prior work to leverage the graph structure of the spatio-temporal processes for the viability monitoring. In this paper, we propose a time-vertex signal processing framework for the irregular thermal data of the pure liver region monitoring. In particular, we extract features of irregular thermal data based on the joint Fourier transform (JFT), which is an integration of graph Fourier transform (GFT) and discrete Fourier transform (DFT). The extracted JFT features can accurately reconstruct the thermal images with a limited number of features. Then, we use a non-parametric online change-point estimation method, based on online scan B statistics, to monitor the JFT features without a parametric distribution. Our proposed framework is applied to both simulation and the liver procurement data, and achieves good monitoring performance. [ABSTRACT FROM AUTHOR]